NUMERICAL TECHNIQUE FOR SOLVING KLEIN-GORDON EQUATIONS WITH PURELY INTEGRAL CONDITION

The present paper is devoted to a proof of the existence, uniqueness, and continuous dependence upon the data of solution to a klein gordon equation with purely integral conditions. The proofs are based by a prioriestimate and numerical technique. We present a numerical approximate solution to a klein gordon equation with integral conditions. A Laplace transform method is described for the solution of considered equation. Following Laplace transform of the original problem, an appropriate method of solving differential equations is used to solve the resultant time-independent modified equation and solution is inverted numerically back into the time domain.Numerical results are provided to show the accuracy of the proposed method.